Question

36. For the one-dimensional harmonic oscillator with a force constant $k$ and frequency $\omega$ in the ground state, determine: (a) $\langle x \rangle$ (b) $\langle x^2 \rangle$ (c) $\langle p \rangle$ (d) $\langle p^2 \rangle$ 38. Using the results from the problem 36, find the average values of potential and kinetic energy, $\langle V \rangle$ and $\langle T \rangle$, for a harmonic oscillator in the ground state. Express each in terms of the zero-point energy $E_0$.

          36. For the one-dimensional harmonic oscillator with a force constant $k$ and frequency $\omega$ in the ground
state, determine:
(a) $\langle x \rangle$
(b) $\langle x^2 \rangle$
(c) $\langle p \rangle$
(d) $\langle p^2 \rangle$
38. Using the results from the problem 36, find the average values of potential and kinetic energy, $\langle V \rangle$
and $\langle T \rangle$, for a harmonic oscillator in the ground state. Express each in terms of the zero-point energy
$E_0$.

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36. For the one-dimensional harmonic oscillator with a force constant k and frequency ω in the ground
state, determine:
(a) ⟨ x ⟩
(b) ⟨ x^2 ⟩
(c) ⟨ p ⟩
(d) ⟨ p^2 ⟩
38. Using the results from the problem 36, find the average values of potential and kinetic energy, ⟨ V ⟩
and ⟨ T ⟩, for a harmonic oscillator in the ground state. Express each in terms of the zero-point energy
E0.

Added by Brittany M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Keshav Singh

08/12/2021

Step 1

Step 1: From problem 36, we know that in the ground state of a harmonic oscillator, the expectation value of position <x> is 0, the expectation value of x^2 is (hbar/2mω), the expectation value of momentum <p> is 0, and the expectation value of p^2 is (mωhbar/2). Show more…

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PLEASE ANSWER PROBLEM 38. Problem 36 provided for context. 36. For the one-dimensional harmonic oscillator with a force constant k and frequency o in the ground state, determine: (@)(x) (b)(x2) (c)(p) (d) (p2) 38.Using the results from the problem 36, find the average values of potential and kinetic energy,(V and (T), for a harmonic oscillator in the ground state. Express each in terms of the zero-point energy Eo.

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